Formulas

• The average value of a continuous function `f` on `[a,b]` is

  ${\displaystyle \frac{1}{b-a}{\int }_a^{b}f\left(t\right)dt\mathrm{.}}$

• An antiderivative of a continuous function `f` on `[a,b]` is

  ${\displaystyle F\left(x\right)={\int }_a^{x}f\left(t\right)dt}$   for  `a ≤ x ≤ b`.

• If `f` is a continuous function on `[a,b]`, then

  `int_a^b ftext[(]t text[)] dt = ``int` `ftext[(]t text[)] dt |_a^b`.